At the start of the twentieth century the structure of the atom was still a puzzle. The turning point came in 1911, when Ernest Rutherford, bombarding thin gold foils with alpha particles, experimentally showed that almost all of the atom’s mass and all of its positive charge are concentrated in a tiny, extremely dense nucleus, around which the electrons move. This gave rise to the “planetary” model: a miniature solar system in which the electrons orbit the nucleus like planets around the Sun.
The model was intuitive and explained the scattering results well, but it hid a dramatic problem, one that classical electromagnetism made unavoidable.
The paradox of classical instability
According to classical electromagnetism, an accelerated charge radiates electromagnetic waves. An electron in a circular orbit is constantly accelerated (centripetal acceleration), so it should continuously emit energy, slow down and spiral into the nucleus in less than s.
The reckoning is merciless: if classical laws also held at the atomic scale, no atom would survive more than a tenth of a billionth of a second. Yet the atoms around us have been stable for billions of years. This contradiction between theory and the most trivial evidence — the very existence of matter — was one of the great mysteries of physics.
The key to escaping it is a radical idea, which shifts the problem from the language of particles to that of waves. If the electron is not a point following a trajectory, but a wave spread around the nucleus, then it cannot settle into just any orbit: like a guitar string that vibrates only at certain frequencies, the electron’s wave can “exist” only where it closes neatly back on itself. The allowed orbits become few and discrete, not a continuum: this is quantisation. This is where Bohr’s model starts, and the most natural way of justifying it comes precisely from the picture of the electron as a standing wave.
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Topics: Quantum physics Concepts: Bohr model Objects: Hydrogen atom
Related exercises: Hydrogen levels, Balmer and Lyman · Derive the radius of the Bohr orbit · Worked exercise — a red photon from the hydrogen atom